Summary. "Max pain" is the settlement price that minimizes the total payout to option holders. It is widely cited and often misunderstood. This article separates two ideas that are usually mixed together: max pain as an accounting quantity, and pinning as a hedging effect documented in the academic literature. A stylized simulation shows how long-gamma hedging near a large strike concentrates closing prices, and the article lists the conditions under which pinning is more and less likely.
1. Max pain as an accounting quantity
For a settlement price , the total intrinsic value paid to holders of open options is
Max pain is the that minimizes . Because is piecewise linear and convex in , the minimum always falls on a listed strike. Figure 1 shows the curve for the hypothetical chain used throughout this series; its minimum is at 6,000.
Max pain says nothing about who holds the options or how they are hedged. It is not, by itself, a mechanism. The popular claim that dealers "push price to max pain to minimize their losses" assumes dealers are short all of the open options, which is not the case under the usual convention (dealers long calls, short puts) and ignores that hedged dealers are largely indifferent to the settlement price.
2. Pinning as a hedging effect
Pinning is the tendency of the underlying to close near a strike with large open interest on expiration day. It has a well-documented mechanism. Avellaneda and Lipkin model a stock whose market makers are net long options at a strike and show that their delta hedging produces a drift toward the strike, with a positive probability of closing exactly there [1]. The intuition follows from the hedge rule: a long-gamma dealer sells as price rises above the strike and buys as it falls below, and the size of those trades grows as expiry nears because gamma near the strike scales with .
The empirical evidence is consistent with this. Ni, Pearson and Poteshman show that stocks with listed options close near strike prices on expiration dates significantly more often than on other days, and attribute the effect to delta hedging by market makers and to trading by firm proprietary traders [2]. Golez and Jackwerth find that S&P 500 futures move toward at-the-money strikes on expiration days of the serial futures options, and estimate that the price shift represents at least $115 million of futures notional per expiration [3].
3. A stylized simulation
To illustrate the mechanism, suppose dealers are long 30,000 contracts at the 6,000 strike on its expiration day. Each five-minute return is an exogenous shock divided by a hedging factor, using the price-impact logic in the volatility trigger article:
With there is no hedging impact. With , moves shrink near the strike, and they shrink more as expiry approaches. Figure 2 shows the closing distance from the strike over 4,000 simulated sessions starting within 20 points of 6,000.
Without hedging impact, about 6% of sessions close within 5 points of the strike and about 26% within 20 points. With long-gamma hedging, those shares rise to about 27% and 92%. The parameters are illustrative; the qualitative result is the point. Pinning requires two things: dealers must be long gamma at the strike, and the strike must be close enough that its gamma is large when expiry approaches.
4. When pinning is more likely
- Dealers long gamma at the strike. If customers bought the options at that strike, dealers are short gamma there, and hedging pushes price away from the strike rather than toward it.
- Concentrated open interest. One dominant strike creates a single attractor. Similar open interest at adjacent strikes splits the effect.
- Proximity late in the day. The relevant distance shrinks as expiry approaches. Late in the session a strike more than about one remaining standard deviation away has little gamma left.
- Quiet macro calendar. Exogenous flow dominates hedge flow on event days.
5. When it breaks
- Short-gamma regime. Below the gamma flip, aggregate hedging amplifies moves, so local pins are weaker.
- Scheduled events during expiration week. FOMC decisions, CPI and payroll releases add a jump to the price path that hedging cannot absorb.
- Directional option demand at a different strike. Heavy customer buying elsewhere can leave dealers short gamma near spot.
- Thin liquidity. Hedging only pins price if hedge trades move it. Holiday sessions reduce both hedging and other flow, so the outcome is less predictable.
6. Using the concept
Max pain is a convenient summary of where open interest is concentrated, and it often lies near the largest strikes. The quantity that matters for pinning, however, is dealer gamma at specific strikes, its sign, and its distance from spot as expiry approaches. A practical sequence:
- Identify the large strikes near spot for the expiring contracts and estimate the dealer side.
- Check whether spot is above the flip and whether the dominant strike carries positive dealer gamma.
- Measure the distance from spot to that strike in units of the remaining expected move.
- Re-check in the early afternoon. A shrinking distance with stable positioning is consistent with a forming pin; a widening one is not.
DataFirst's pin risk view combines these inputs into a single score.
For educational and informational purposes only. Not financial advice. Options trading involves substantial risk of loss. The chain and simulation are hypothetical and illustrate mechanics only.
References
- Avellaneda, M., & Lipkin, M. D. (2003). A market-induced mechanism for stock pinning. Quantitative Finance, 3(6), 417–425. doi.org/10.1088/1469-7688/3/6/301
- Ni, S. X., Pearson, N. D., & Poteshman, A. M. (2005). Stock price clustering on option expiration dates. Journal of Financial Economics, 78(1), 49–87. doi.org/10.1016/j.jfineco.2004.08.005
- Golez, B., & Jackwerth, J. C. (2012). Pinning in the S&P 500 futures. Journal of Financial Economics, 106(3), 566–585. doi.org/10.1016/j.jfineco.2012.06.010